The information was stored on a computer hard drive, which was taken when a doctor's home was burglarized.
The hard drive was taken in September, but it took investigators several weeks to identify and locate the patients affected by the burglary.
The medical records in question range from July 2007 to July 2011.
UCLA sent letters to the 16,288 patients affected, warning them of possible identity theft and giving them contact information for a data security company the system has enlisted for help.
The documents included birth dates, addresses and medical record numbers and medical information, but no Social Security numbers or financial information, and no patient's complete medical records were on the hard drive, officials said.
The UCLA system includes Ronald Reagan UCLA Medical Center, Mattel Children's Hospital, Santa Monica UCLA Medical Center and Orthopedic Hospital, and Resnick Neuropsychiatric Hospital, along with outpatient clinics.
Officials said there is no evidence that the records have been accessed.
The Associated Press contributed to this report.